91影视

1. Speed of sound in metal is$\mathrm{v}$ .
2. Speed of sound in metal is${\mathrm{v}}_{\mathrm{m}}$.
3. Length of tube is$\mathrm{L}$ .

Using the formula of velocity, we can derive the equation for the time interval between the arrivals of the two sounds at the listener鈥檚 ear if v is the speed of sound in air. Using this derivation, we can find the length of the pipe.

Formula:

The velocity of the sound wave,

$\mathbf{v}\mathbf{=}\mathbf{d}\mathbf{/}\mathbf{t}$ 鈥�(颈)

Using equation (i), we can the time taken by the body to be:

$\mathrm{t}=\frac{\mathrm{L}}{\mathrm{v}}$

$鈭�\mathrm{d}=\mathrm{L}$

Time t for sound to travel in the metal is${\mathrm{t}}_{\mathrm{m}}=\mathrm{L}/{\mathrm{v}}_{\mathrm{m}}$

Time t for sound to travel in air is${\mathrm{t}}_{\mathrm{a}}=\mathrm{L}/\mathrm{v}$

So, the time interval between these sounds can be given as:

$\begin{array}{c}\mathrm{螖迟}={\mathrm{t}}_{\mathrm{a}}鈭�{\mathrm{t}}_{\mathrm{m}}\\ \mathrm{螖迟}=\frac{\mathrm{L}}{\mathrm{v}}鈭�\frac{\mathrm{L}}{{\mathrm{v}}_{\mathrm{m}}}\end{array}$

$\mathrm{螖迟}=\frac{\mathrm{L}({\mathrm{v}}_{\mathrm{m}}鈭�\mathrm{v})}{{\mathrm{v}}_{\mathrm{m}}\mathrm{v}}$ 鈥�(补)

Therefore, the time interval between the arrivals of the two sounds at the listener鈥檚 ear if $\mathrm{v}$is the speed of sound in air is $\frac{\mathrm{L}({\mathrm{v}}_{\mathrm{m}}鈭�\mathrm{v})}{{\mathrm{v}}_{\mathrm{m}}\mathrm{v}}$.

We have the length of a material using equation (a) as:

$\mathrm{L}=\frac{\mathrm{螖迟}}{\left(\frac{1}{\mathrm{v}}鈭�\frac{1}{{\mathrm{v}}_{\mathrm{m}}}\right)}$

For metal that is for steel pipe, ${\mathrm{v}}_{\mathrm{m}}=5941\text{鈥尘}/\text{s}$and as $\mathrm{v}=343\text{鈥尘}/\text{s},\mathrm{螖迟}=1.00\text{鈥塻}$.

Hence, the length value is given as:

$\begin{array}{c}\mathrm{L}=\frac{1.00\text{鈥塻}}{\left(\frac{1}{343\text{鈥尘}/\text{s}}鈭�\frac{1}{5941\text{鈥尘}/\text{s}}\right)}\\ =364\text{鈥尘}\end{array}$

Therefore, the length $L$, if $\mathrm{螖迟}=1.00\mathrm{s}$and the metal is steel is$364\text{鈥尘}$ .